solution of

(sin^4theta - cos^24theta)=(7/2)sintheta costheta

did you really mean cos^24x???

sin^4(x) - cos^4(x) = 7/2 sinx cosx
didn't we just do this?
sin^4x - cos^3x) = (sin^2x + cos^2x)(sin^2x - cos^2x) = -cos(2x)
and see your other post